Other Blogs And Books

Here is a quick look at my other blogs before you start this one.

My main blog, where the most recent postings on all topics are to be found, is http://www.markmeeksideas.blogspot.com/

If you liked this blog on progress, you will also like my blog about economics, history and other human issues, http://www.markmeekeconomics.blogspot.com/

http://www.markmeekearth.blogspot.com/ is my geology and global natural history blog for topics other than glaciers. http://www.markmeekworld.blogspot.com/ is my natural history blog concerning glaciers.

http://www.markmeekniagara.blogspot.com/ is about new discoveries concerning natural history in the general area of Niagara Falls.

http://www.markmeeklife.blogspot.com/ is my observations concerning meteorology and biology.

http://www.markmeekphysics.blogspot.com/ is my blog about physics and astronomy.

http://www.markmeekcosmology.blogspot.com/ is my version of string theory that solves many unsolved mysteries about the underlying structure and beginning of the universe.

http://www.markmeekpatterns.blogspot.com/ details my work with the fundamental patterns and complexity that underlies everything in existence.

http://www.markmeekreligion.blogspot.com/ is my religion blog.

http://www.markmeekcreation.blogspot.com/ is proof that there must be a god.

http://www.mark-meek.blogspot.com/ is my autobiography

http://www.markmeektravel.blogspot.com/ is my travel photos of North America.

http://www.markmeekphotos.blogspot.com/ is my travel photos of Europe.

My books can be seen at http://www.bn.com/ http://www.amazon.com/ or, http://www.iuniverse.com/ just do an author search for "Mark Meek"

The Idea Curve

In my economics blog, I explained the present (2009) economic distress in terms of economics. I have another explanation of it on a deeper level. This second and deeper explanation is unrelated to economics and has nothing to do with politics.

Plainly and simply, globalization has hit home and has done so with quite a bit of force. The recent economic events that began in the U.S. and spread outward through the western countries are actually a downward correction in the living standards of the west relative to the rest of the world. The truth is that there is no economic justification for people in the western countries to have a vastly higher living standard than the rest of the world.

Let's compare these economic calamities to an earthquake. Two tectonic plates inside the earth are exerting a force on each other as they move in opposite directions. One plate is the Western Plate, representing the living standards of the western countries. The other plate is the Eastern Plate, representing the rest of the world.

The economic shock that has just happened and is continuing represents the Eastern Plate slipping forward while the Western Plate slips backward. The ever-growing popularity of deep discount stores in the west like Wal-Mart and Aldi's represent the inevitable sliding of the standard of living. It is as I described it in my book "The Commoner Syndrome".

Most people in the west work at jobs that could be done anywhere in the world or could at least be done by most anyone from anywhere in the world. So given the laws of supply and demand, there is absolutely no economic justification for the west to have a far higher living standard. Most manufacturing as well as anything that can be done by computer or telephone can be done much more cost-effectively from Asia. Outsourcing reaches further every year and now includes medical operations and legal work done from India.

There is just no way the west is going to go on with it's present standard of living the way things are going. The only way for the west to continue with the present relative standard of living is what I will call the "Idea Curve".

The east can generally do things much more cost-effectively than the west because people are willing to live with less. But the west has something that it does best. The west gives the world virtually all of it's new ideas in the modern age. It is in North America or Europe that virtually all of the technological progress has originated over the past few hundred years.

The reason that the western standard of living is slipping is that we are slowing down on the Idea Curve. This curve is the rate at which the western countries must come up with breakthrough new ideas and technology to keep it's standard of living relative to the rest of the world.

In my opinion, the next major technological step we should be working on is solar power. When a new technology emerges in the west, sooner or later a way will be figured out to manufacture it more cost-effectively in the east. But if the west can keep coming up with breakthrough new technology, by the time those industries move eastward there will be new technology to take it's place. It is only in this way that the western countries can keep their relative standards of living.

The underlying reason why the west is slipping backward is that reading and learning is more valued in many other countries than it is here. If people in other parts of the world are enthusiastically studying while we are watching nonsense on television then this slide will continue. The west needs not just educated people and hard workers because the rest of the world has that too, it needs breakthrough new technologies emerging at a much faster rate than at present. That is one of the reasons for this series of blogs, to promote interest in science and progress.

The Scan Method Of Computer Encoding

I am burdened with an extreme sense of efficiency. When I was young, I never seemed to have enough time to do all of the reading and exercise that I wanted to do and so I was always looking for ways to make things more time-efficient. This gave me a sense of efficiency that applied to everything.

One thing that I have written about before as being inefficient in the extreme is the ASCII system used to encode the alphabet, punctuation and, control characters for computing. In this outmoded system from 1968, eight bits is defined as a byte. Since each bit can be recorded as either a 1 or a 0, that means there are 256 possible combinations for a byte because two multiplied by itself eight times equals 256. These 256 possible combinations in a byte are used to encode the letters of the alphabet as well as punctuation and unprinted control codes, such as carriage return.

I have written quite a bit about ways to upgrade this system to make it more efficient, and it seems that every time I see it I notice yet another way that it could be improved. We could gain a lot of efficiency by agreeing on an order of all of the byte codes used in ASCII. We have an order for the letters of the alphabet, and the same concept can be applied to all of the codes.

Once we agreed on a sequential order for all of the byte codes used in ASCII, we could scan any document that was to be encoded to see which codes were present in the document. A typical document may not include letters like Q and Z or characters such as +, =, !, #, etc. The first 256 bits of an encoded document would be to indicate, in sequential order, which of the byte codes were present in the document.

Then, for each present byte code, there would be a line of bits which could each be set to a 1 or a 0. These bits would be scanned to reproduce the document and would indicate whether that present character was included in this scan. A scan of the first bit after each present character would be the first scan, a scan of the second bit after each present character would be the second scan, and so on.

The system would be programmed to first, separate out the first 256 bits which indicate which characters are present. Then, to divide the remaining bits by the number of present characters. This division would yield an even number which would be the number of scans that would be needed to be done to replicate the document. If a scan bit for a particular present character is set to 1, that would mean that the character is included in that particular scan and a 0 if it is not. There would, of course, be as many scan bits as necessary after each character to complete the document.

This method would not be efficient with a single sentence. "I went to the store" would require eleven scans of ten present characters, including the space between words. Each scan would scan the present characters in the agreed-upon order of the byte codes so that this sentence, with it's eleven scans and an underscore to show the spaces between words, would look like this:
I_
w
ent
_t
o
_t
h
e
_st
or
e
Since the present byte codes would be scanned in the agreed-upon sequence, we cannot go backwards in the alphabet or double letters, another scan would be necessary. Since spaces occur so frequently in written documents, we can replace some of the non-present characters with spaces to make the process still more efficient.

This is not efficient with a single sentence but, unlike ASCII, the efficiency compounds as the document gets longer because more letters would be included in each scan. With an extremely long document, we would approach a condition of efficiency in which each letter and character would be expressed with a single bit, rather than the eight bits of the ASCII system. In contrast, ASCII gets no more efficient as the document gets longer.

We are making so much progress with processor speeds and drive capacity, but are still using the utterly inefficient coding system that has been in use since the ancient history of computing.

The Amateur Wave

One way to help predict the future of trends in everyday technology is what I will term the "Amateur Wave". Amateurs have a vital role in the development and assimilation of new technology. As one phase of the Amateur Wave terminates because developments have made it too difficult, as well as unnecessary, a new phase inevitably opens up somewhere else.

Solid state (meaning based on transistors and other chips, rather than vacuum tubes) technology, combined with mass-production techniques, made small radio devices very difficult to diagnose and repair, and at the same time inexpensive enough to be disposable so that repair was unnecessary. It cost less to simply buy a new transistor radio, than to try and repair a broken one.

But prior to these developments, the Amateur Wave contributed a tremendous amount to the development of electronics and radio technology, from amateur (HAM) radio operators to the hobbyists who would construct all manner of projects from kits and electronic components. A few decades ago, skill with electronics was in very high demand.

Just as mass-production and miniaturization was making that increasingly unnecessary, more and more people were becoming able to afford cars, and the Amateur Wave shifted into the automotive field. From the  1950s to the early 1980s, one might hear a guy talking about rebuilding the engine of his car over the weekend, or fine-tuning it's performance in the days when engines still required tune-ups, or maybe installing an air intake scoop on the hood to impress everyone at school.

But then cars got more efficient and computerized so that, as with electronics and radios in earlier days, amateur participation became increasingly difficult as well as unnecessary.

It was around this time that computers were making the transition from mainframes to PCs, and the Amateur Wave moved on to another phase. In a technically-inclined family, the grandfather might reminisce about building radios and electronic projects, the father about souping up car engines and, the son about putting together computers and adventures online and with computer games.

Whatever the next major development in technology turns out to be, we can be sure that the Amateur Wave will be there.

The Next Hobby

I have an interesting idea for a hobby that should be technically possible now. Why not observe, follow the orbits of, and possibly photograph satellites? Those familiar with amateur astronomy have probably noticed that satellites can periodically be seen going over. A satellite, if seen from the ground, appears as a star that is moving at a steady pace. One way to differentiate a satellite from an aircraft is obviously that the satellite will have no blinking lights. Satellites must be much higher than aircraft so that they will not be destroyed by friction with the atmosphere.

There is a certain window of time each day during which satellites can be seen. It must be after the sun has set and it is dark, but not too long after the sun has set. To be visible, it must be dark where the observer is but the sun must still be shining on the satellite. A satellite would not be visible from the ground in the middle of the night because you would be on the opposite side of the planet from where the sun is shining.

Satellites orbit the earth in either a polar, over the poles, or an equatorial, above the equator, orbit. I live at 43 degrees north, almost halfway to the north pole from the equator. This means that I can see satellites moving along a north-south line in a polar orbit, but I am too far away from the equator to see satellites in an east-west equatorial orbit.

I have seen satellites moving along, until suddenly disappearing from view. The reason is that the earth is rotating and the sun was suddenly no longer shining on the satellite.

One night, there was a full moon. I noticed a satellite moving until it suddenly disappeared. But, on looking closely, I noticed that the satellite was still very faintly visible. I had never noticed this before and it was because the satellite was out of the sun but was reflecting the moonlight.

The Concept Of Fluid Pricing

This is about another possible major application of computer technology. Stock trading is already computerized, and I think that there is tremendous potential for use of computer technology to facilitate the smooth operation of the economy as a whole.

The idea of a market economy began, as we might expect, with markets. The type of traditional markets that have operated in town squares for thousands of years. In such traditional markets, there was no such thing as an artificial recession. Any reductions in economic activity were caused only by outside factors, such as drought or warfare.

The wonderful thing about a market economy is that it enables us to fill our potential, to economically "do all that we can do". An economy must be balanced between it's supply and demand sides to continue functioning, any changes in either supply or demand can disrupt this balance.

When this happens, to keep the economy running smoothly, it must be quickly brought back into balance. The traditional market deftly accomplishes this by haggling, the seeking of an agreeable price between buyer and seller.

We get our well-known "Law of supply and demand" from these traditional markets. When demand rises relative to supply, prices rise. When supply increases relative to demand, prices drop. The goal of the economy is to produce all that the people need, and will buy, and to leave nothing unsold.

We have adapted the market concept from the town square as the basis of the modern economy. As you may notice, things do not always work smoothly. There are periodic recessions, or cutbacks in production and economic activity, that are very harmful. It is a really absurd situation when, for example, a family is struggling to keep and old car running because they cannot afford a new one, while down the street there is a car dealership letting employees go because so few people are buying cars. Most of these recessions are artificial recessions and are not caused by outside factors beyond our control.

The truth that I want to point out is that we do not have a genuine market economy. The hinge upon which a true market functions is the haggling between buyer and seller to arrive at an agreeable price. This was discussed in the posting "Recessions Made Really Simple" on my economics and world issues blog, www.markmeekeconomics.blogspot.com . This continuously maintains the essential balance between the supply and demand sides of the economy.

There is a form of haggling done on a global scale, since the prices of oil, other commodities and, national currency exchange rates are usually reset on a daily basis. The selling price of cars also tends to be open to a certain amount of haggling. But in the stores where ordinary consumers shop, it is quite a different story. Prices are indicated on the product and the shelf with a label or price sticker. Prices do change, to reflect the law of supply and demand, but this is not done continuously.

Decisions to change prices, when necessary, is done at the management or corporate level. This takes time, and it is in this delay in responding to continuously-changing supply and demand that the seeds of recession are planted. This slowness to change prices is known to economists as their "stickiness".

By the way, one thing that I think Reagan-era Republicans had right is their terminology. Referring to the "supply side" (business) and the "demand side" (consumers) is much more descriptive than referring to the two sides as "liberal" and "conservative".

In the posting, on the economics blog, "Recessions Made Really Simple", I explained how an increase in production can actually bring about a recession. Unless there is a corresponding increase in wages, there will not be enough money in circulation to buy all of the goods and services that have been produced. Since it does not make sense to produce goods or services that are not going to sell, companies tend to cut back on production when demand seems to fall. This means letting go of workers, who then have less money to spend on consumer goods, thus furthering the recession spiral.

This beginning of a recession could be remedied by a lowering of prices. This would re-establish the balance between the supply and demand sides of the economy, that was upset by the change in the relative positions of production and demand.

Companies are reluctant to lower prices since this will cut into expected revenue. But, with the economy as a whole, this reluctance means that the correction to keep the economy balanced when there is a change in the equilibrium between the supply and demand sides caused by increased production, without a corresponding increase in wages, must come from another direction.

Unfortunately, the correction then comes in the form of a cutback in production, because the newly-increased level of production is not balanced by the wages on the demand side. This begins the downward spiral that we refer to as a recession.

The old practice of haggling, as practiced in traditional marketplaces, would solve all of this by continuously resetting the balance between supply and demand. But haggling is simply not practical in the supermarket and big box store chains of today. Haggling only makes sense when the merchant actually owns the goods, or at least is working on commission. Cashiers and clerks in stores cannot be expected to haggle with customers over prices, many would likely be accused of giving away merchandise to their friends and families.

However, in recent years store records have become computerized. We all know that the real reason that stores give out bonus cards, with a magnetic strip, is so that they can track who buys what. Stores using bar code technology on products keep databases on the volumes of each item sold. This is matched with an inventory record of the goods.

The root of the trouble is that the pre-determined prices of the goods are too slow to change, whereas this would not be the case in a traditional market, based on haggling. Why not apply computer technology to bring the haggling mechanism back?

A program could keep track of the sales of every product. If the product was not selling well, relative to it's previous sales and inventory in stock, the program would try lowering it's price. Instead of the standard price displays on the shelves, new digital price displays would be used and would be connected to the central pricing system.

Prices would be automatically reviewed weekly in supermarkets, daily in smaller stores and, maybe monthly in stores selling larger items. The volume per purchase would be taken into account, it would count as "less" of a sale if one customer bought five of a certain item than if five customers each bought one, because the purchase of five may be less reflective of true sales trends. Total sales in the store would also have to be considered, since something like a severe storm would mean that there would be fewer shoppers than average in the store. A certain upper and lower limit could be pre-set for the price of each item.

Companies would, of course, lose revenue when prices are lowered, but this would usually be preferable to the items not selling at all, especially when it comes to perishables. But in the same way, these losses could be recouped by edging up the prices of those items that were selling well.

Supposedly, the benefit of a market economy is that economic decisions are made, in effect, by all consumers, not just by a few central planners as in a command economy such as Communism. Yet, our existing pricing system more resembles an inefficient command economy in that it has lost the advantage of haggling, as in a traditional market, and must wait for management to make decisions on pricing.

Running an economy without fluid pricing is a lot like trying to run a car engine without oil. Sooner or later, the economy seizes up. The "oil" of a true market economy is the fluidity of pricing which characterizes a traditional market based on haggling. I believe that computer technology has made it possible to incorporate a form of haggling into the economy, so that we can stave off these destructive recessions. Another possible way is, as I suggested in "Recessions Made Really Simple", the manipulation of payroll taxes by the government to ensure that the supply and demand sides of the economy remained in balance when there is an increase in production, while wages still lag behind.

The Keypad System Of Global Navigation

I have long been thinking that there must be a better way to define points on the earth's surface than the system of latitude and longitude that has been in use for centuries.

Here is a question for you. Without looking at a map, what is your latitude and longitude? If you are like the vast majority of people in the world, you do not have the slightest idea of what the latitude and longitude coordinates are where you live. In fact, there are very few people who actually use latitude and longitude.

Latitude and longitude was a revolutionary development at the time as a method of pinpointing a location anywhere on earth. The earth is a sphere and latitude is the location of a point on the surface in degrees north or south of the equator so that the equator represents zero degrees, the north pole is 90 degrees north and the south pole is 90 degrees south. Lines of latitude are also known as parallels. It is easy enough to measure one's latitude by measuring the apparent angular altitude of the north star above a flat horizon.

Measuring longitude is more difficult. Longitude is the degrees east or west and a line of longitude is also known as a meridian. The best way to measure longitude is by time. Britain's John Harrison developed a very accurate clock that was not based on the motion of a pendulum. Clocks based on a pendulum were considered as unreliable at sea because the pitching and rolling of the ship in rough water might affect the timing of the pendulum.

Longitude could then be measured by keeping a clock set to Greenwich Mean Time (GMT) on the ship and then measuring local solar time by means such as a sun dial. The difference would be the ship's longitude. The north-south line through the observatory in the London suburb of Greenwich was defined as the Prime Meridian, which represents zero degrees longitude. If local solar time was ahead of GMT, the ship must be east of the Prime Meridian and would be west of the Prime Meridian is it was behind GMT.

You may have heard of a so-called "nautical mile" that is used at sea. This nautical mile is defined by the sphere of the earth and is one-sixtieth of a degree of latitude or of longitude at the equator, it is equal to 1.16 statue miles. A "knot" is a reference to speed, meaning one nautical mile per hour.

The trouble is that while latitude and longitude was revolutionary in it's day, it is not really user-friendly. The real difficulty is that we are used to dealing with square maps, and since the earth is a sphere it's surface cannot be rendered with complete accuracy on a square map. There is equal distance between lines of latitude, but the distance between lines of longitude vary according to latitude. Meridians are furthest apart at the equator, the same distance apart as lines of latitude, but converge at the poles. Various methods of projection have been developed for mapping the entire earth, but all must necessarily involve either breaks or distortion.

One reason that latitude and longitude is not user-friendly concerns our number system. It is based on a 360-degree circle because 360 is a nice, round, easily-divisible number. Our number system is based on ten, because people have ten fingers, which is not a nice, round, easily-divisible number. The result is that latitude and longitude coordinates cannot be easily rendered into the decimal system that we are used to. I covered this in detail in "The Queen of Numbers", on the progress blog. It may be that one of the greatest mistakes ever made by humans is counting by tens instead of twelves, because 12 is much more divisible.

I would like for the earth's entire surface to be rendered as squares to be mapped. This is not possible to do with accuracy if the equator extends across the middle, as we are accustomed to. The approach that I want to take is to put the equator diagonally across squares so that the equator extends from upper right to lower left, instead of laterally across the center.

Suppose that we divide the circumference of the earth into thirds along the equator. Under my system, each third will be the diagonal of one of nine squares that will cover all of the earth's surface. The squares will be imposed on the earth's surface as nine four-sided diamonds with the equator being the diagonal of the three squares that are a diagonal across the middle, from upper right to lower left.

The equator will be the diagonal of three squares, there will be two squares in the spaces between these three squares, on each side of the equator, and one square in the space between these two squares. This will bring us to a total of nine squares that will cover the entire surface of the earth. The north and south poles will each be in the center of the one square in the space between the two squares.

Now, do you notice that these nine squares are identical to the keypad on a phone or computer? That is why this is called the keypad system.

Suppose that we now take each of our nine squares, that cover the entire surface of the earth, and subdivide it into nine squares? We can easily express any square with it's number, from 1 to 9. Then, with each square subdivided into nine squares, we can also express that with a number. So, if the first square is 5 and the square within it is 9, we would express that portion of the earth's surface as 59. Nice and simple.

This could be a modern system of navigation designed for expression via a keypad, since it is designed to match the numbers on a keypad. The concept also fits perfectly with the philosophy of the metric system.

We can then subdivide the second, inner, square also into nine sqaures. Then, we could further divide all of those squares into nine squares. By doing this, we can narrow down the area of the earth's surface as much as we like or as much as we are able to. The more numbers in the expression, the more accuracy and the smaller the square. 5391684 will represent much more accuracy than 5391.

The number of a particular location could be entered into satellite imagery software and would bring up the designated square on the earth's surface automatically. It would also be much easier to get an idea of the distance between two points. This can be done with latitude and longitude, but involves calculation (For my formula, see "The Geographic Formula" on this blog).

Notice that the squares are only number from 1-9. This leaves us with the zero to separate the numbers of multiple squares that are designated. For example, 346206851 would mean squares 3462 and 6851. If an area that we want to designate does not fit neatly with these squares, we can easily define the points that do signify the area that we want to designate by separating them from one another with zeros.

This system would be much more convenient than latitude and longitude, particularly with there being so much technology using keypads.

The "Subtract One" Rule

Most of the expression of the odds, or chances, of something happening involves simple odds that can be expressed as an ordinary fraction. There are seven days in a week, one of those days is Tuesday. So if we choose at random a day in the past or future, there is a 1/7 chance that the day will be a Tuesday.

But, I find that odds are often more complex than that and involve what I call "The Subtract One Rule". I would like to give my version of complex odds.

Suppose that, in a town, there are 6 red cars, 3 white cars and, 25 blue cars. There is a random collision between two cars. What are the odds that the collision involved two cars of the same color (colour)?

There are 34 cars altogether. So we would, subtracting one from both numerator and denominator, multiply 6/34 x 5/33 for the red cars. Multiply 3/34 x 2/33 for the white cars. Multiply 25/34 x 24/33 for the blue cars, and then add the three products together. This gives us the odds of the collision being between cars of the same color (colour) as 636/1122, or nearly 57%.

It is necessary to subtract one from both numerator and denominator as we proceed because after we have the first car, there is one less car both in the ones of that particular colour (color), and also in the total number of cars.

An ideal example of this rule was given in the posting about granularity on the progress blog, involving pairs of gloves in a drawer. Suppose that there are ten gloves in a drawer, five right gloves mixed with five left gloves. If you reach in and pull out two gloves without looking, what will be the odds that you will have a matching pair?

Your first answer might be 50/50, or even odds of pulling out a matching pair. But this is not correct. When you take the first glove, whether it is right or left, that will leave four that will not be a match with it but five that will. So, the odds are actually 5/9 that you will pull out a matching pair. We must remember to "subtract one" from the total so that the odds are 5/9, instead of an even 5/10. The odds would be even only if there were an infinite number of gloves in the drawer.

We also must remember to subtract one in order to find the odds of the collision involving two cars of any given colour (color). There are only three white cars so that the chances of a random collision being between two white cars is a slim 3/34 x 2/33. This is because once the first car is white, there will be only two white cars remaining, so that we must remember to "subtract one". The odds of the collision involving two white cars is thus 6/1122, or just over one half of one percent.

If there were a random three-car collision, the odds against all three cars being white would be an extremely slim 3/34 x 2/33 x 1/32, or 6/35904 which is equivalent to 1.67 out of a thousand.

To find the odds of a random two-car collision involving one of the six red cars and one of the three white cars, we have to multiply fractions as well as subtracting one. The odds of a white car being the first car is 3/34. Then, the odds of the second car being a red car is 6/33. This gives us 18/1122, or about 1.6%. Notice that this is three times the odds of the collision involving two white cars because there are three times as many red cars as white cars available as the second car after subtracting the first white car.

Mathematics And Matter

In the posting "Matter In Space And Numbers", we saw that the numbers that we commonly use are actually a reflection of the density of matter in space. Aside from addresses and identification numbers the numbers that we use are almost always low, usually less than one hundred, and this is ultimately due to the extremely low concentration of matter in the space of the universe that we inhabit.

Today, let's have a look at how the mathematics which we use are a reflection of the reality that we live in by looking at what it might be like if that reality was different.

We develop mathematics to describe and measure the world around us. If there was nothing, no world and no universe, it would seem that there would be no mathematics. But yet, mathematics are actually the basic patterns of everything. Two plus two always equals four, whether it refers to cars or units of currency. A number itself has no real existence until it is manifested by something, but that does not mean that it does not exist. The number 72,814,932 still exists whether or not there is actually anything which manifests that number.

This can only mean that there is an entire universe of mathematics, of which that manifested by our universe and used by us is actually only a very limited or even an infinitesimal portion. Mathematics, at least as we know it, requires at least two entities with some type of boundary between the two. This most commonly is matter and space.

If we had space but no matter, there could be geometry but what would be the point? There would be nothing to use as reference points. Even to define a straight line, we need two reference points. Any point in the universe would be just as good as any other, there would be nothing to differentiate any place from any other place. With no matter, there would be nothing to count with numbers and no reference points to measure distance from or to.

We could say that we live in a universe in which space is the rule and matter the exception. Suppose that the reverse was true, with matter taking up most of the space. Mapping would be reversed with gaps between matter being charted, rather than the matter itself. Counting numbers would be less important, but angles and distances more important.

Suppose that space was different so that there were no fixed distances. This is related to what we saw in "Straight Lines And The Nature Of Space", on the cosmology blog. This would mean that matter may exist, but it would merge into other matter like clouds, rather than being fixed in location or form. Mathematics would be very different, with measuring rates of change in terms of space against time, predominating. Arithmetic would be of limited use.

If we lived in such a changing cloud-like reality in which matter was not mutually exclusive, the fixed geometry that we know would not make much sense without the ready reference points, but we might define the spaces between objects rather than the objects themselves. With change being much greater than it is in our universe, calculus being used to figure rates of change along with probabilities would be much more important.

Suppose that we had a reality similar to what we have now, but the number of spatial dimensions was different. More dimensions would mean the probability of more change, as well as greater challenges in navigation. It would be easier to get lost, making mapping more important. Reality would generally be more complex, with the basic forces such as gravity and electromagnetism having more dimensions to operate in.

What if all matter was just one "thing", with only one object in the universe? There would be distance measurement and counting, but only if the "thing" manifested some type of suitable reference points. If it was a flat sphere, with no reference points, then measurement and counting would be largely meaningless. Just like a universe of empty space, there would be no reason to map or measure the surface of the sphere if every point on it was the same as every other point. Distance from the sphere into space could be measured, but what purpose would that serve if there was nothing else in the universe to measure the distance to?

If there was no solid matter, but only the fundamental particles, the only mathematics that could be meaningful is rates of change. It would be much easier to measure the effects of the particles on one another, and the changes in these effects, than to count or otherwise measure the particles.

How about if there was no motion, but only stillness? There would have to at least be movement of electromagnetic waves or we could not see to measure anything. Distance measurement would be meaningless if we could not go anywhere. There could be two-dimensional geometry, but not three-dimensional because we could not go anywhere to get a perspective. Neither would there be any time measurement, because motion essentially is time.

Mathematics is a tool to help us in the reality that we inhabit. If we had greater powers, it makes sense that we would have less requirement for tools. If we could multiply things, or bring them into existence at will, we would have no reason to calculate how to do it. If we could move anywhere that we wanted to instantaneously, there would be no need to measure the distance to our destination.